Towards an AI for Dominion

Abstract

Dominion is a modern deck-building game characterized by a combinatorially large state space, imperfect information, indirect player interaction, and stochasticity. Recent successes in artificial intelligence (AI) developed for classical games like Chess and Go, exemplified by AlphaGo and its derivatives, suggest that current machine learning methods may be sufficient to tackle Dominion. We use Upper Confidence Trees (UCT) trained via self-play and a rollout policy modeled by logistic regressors to beat Big Money (BM) in a no-action, two-player, sandbox version of Dominion. We combine the same rollout policy with different parameterizations of UCT to train AI agents in a preset kingdom of full Dominion that match (UCT-F), surpass (UCT-P), and outclass (UCT-DW) the Double Witch (DW) strategy in terms of relative win rate. We highlight the buy strategies of our methods and suggest that UCT for Dominion is bottlenecked by the game's high branching factor of buy decisions, an effect exacerbated by the current lack of suitable value functions for the game.